Affiliation:
1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W Green St., Urbana, IL 61801, USA
Abstract
Given a noetherian abelian k-category [Formula: see text] of finite homological dimension, with a tilting object T of projective dimension 2, the abelian category [Formula: see text] and the abelian category of modules over End (T) op are related by a sequence of two tilts; we give an explicit description of the torsion pairs involved. We then use our techniques to obtain a simplified proof of a theorem of Jensen–Madsen–Su, that [Formula: see text] has a three-step filtration by extension-closed subcategories. Finally, we generalize Jensen–Madsen–Su's filtration to the case where T has any finite projective dimension.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
3 articles.
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1. Tilting Modules and Tilting Torsion Pairs;Springer Proceedings in Mathematics & Statistics;2020
2. The McKay Correspondence, Tilting, and Rationality;Michigan Mathematical Journal;2017-11-01
3. t-Structures on elliptic fibrations;Kyoto Journal of Mathematics;2016-12-01